In Second Language Acquisition, there is an intensive opposition between Grammar-Translation and Natural methods. You can easily find something like this.
Among other, their proponents argue how to supply the students with grammar. I read somewhere that the idea to concentrate on the grammar arose about XV or XVI century, (and from that moment pupils stopped speaking Latin fluently.)
Evidently, Grammar-Translation followers demands that the students have to memorize all declension/conjugation rules. Prominent examples are Dowling’s Wheel or Ranieri-Dowling Method. Wheelock’s course teaches the same rules step by step.
Direct method supposes that the students don’t have grammar tables, but infer all rules by themselves, simply reading (well-prepared) texts. For example, here is how Polis’ Ancient Greek textbook (page 27) introduces the verb εἰμί (to be) in present time:

Some teachers say that it’s more important to memorize vocabulary. If you know every word in a sentence, then you can understand its meaning. In case of poetry with very lax word order, it can be tricky. For example, Boethius, Metrum XII:
Quae sontes agitant metu
Ultrices scelerum Deae,
Jam maestae lacrimis madent.
We can take a paraphrase of these lines made by Callyus for the edition ‘In usum Delphini’:
Deae vindices criminum, quae timore concutiunt nocentes, tristes hument fletibus.
Now, it’s much easier. Reading the original text and its simplified versions, you can accustom to the Latin word order.
In LLPSI, Ørber utilizes both approaches. He gives tables with rules, but also extensively practice them on reading big texts.
Students are different as well. Some are prone to rote-learning, some are better in perception of audio, or learning through action. I personally prefer to read interesting stories (i.e., Graded Readers in the beginning level).
Correct grammar is needed only in Writing. Other three skills—Reading, Listening, and Speaking—do not depend on it much. In spoken language, even in our mother tongue, we make many mistakes but still understand each other.